共查询到20条相似文献,搜索用时 640 毫秒
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Global low-energy weak solution and large-time behavior for the compressible flow of liquid crystals
In this paper, we consider the weak solution of the simplified Ericksen–Leslie system modeling compressible nematic liquid crystal flows in . When the initial data are of small energy and initial density is positive and essentially bounded, we prove the existence of a global weak solution in . The large-time behavior of a global weak solution is also established. 相似文献
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M. Colombeau 《Journal of Mathematical Analysis and Applications》2012,395(2):587-595
We propose a mathematical limit of -stable weak asymptotic methods. A family of -stable approximate solutions is transformed into a normal family of holomorphic functions defined in a complex domain having the real space on its boundary. This provides a holomorphic function which is the same mathematical object as the solutions from explicit calculations. The weak limit of the approximate solutions from weak asymptotic methods in the space of bounded Radon measures is recovered as a boundary value of this holomorphic function. 相似文献
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Christian Bender Peter Parczewski 《Stochastic Processes and their Applications》2018,128(8):2489-2537
Suppose is a Brownian motion and is an approximating sequence of rescaled random walks on the same probability space converging to pointwise in probability. We provide necessary and sufficient conditions for weak and strong -convergence of a discretized Malliavin derivative, a discrete Skorokhod integral, and discrete analogues of the Clark–Ocone derivative to their continuous counterparts. Moreover, given a sequence of random variables which admit a chaos decomposition in terms of discrete multiple Wiener integrals with respect to , we derive necessary and sufficient conditions for strong -convergence to a -measurable random variable via convergence of the discrete chaos coefficients of to the continuous chaos coefficients. 相似文献
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Xianwen Zhang 《Applied Mathematics Letters》2013,26(11):1087-1093
We prove the existence of a global nonnegative weak solution to the Cauchy problem of the Vlasov–Poisson–BGK system for initial datum having finite mass and energy and belonging to with . 相似文献
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Zhuo Min Lim 《Journal of Differential Equations》2018,264(4):2553-2597
We consider the initial-value problem for the Chern–Simons–Schrödinger system, which is a gauge-covariant Schrödinger system in with a long-range electromagnetic field. We show that, in the Coulomb gauge, it is locally well-posed in for , and the solution map satisfies a local-in-time weak Lipschitz bound. By energy conservation, we also obtain a global regularity result. The key is to retain the non-perturbative part of the derivative nonlinearity in the principal operator, and exploit the dispersive properties of the resulting paradifferential-type principal operator using adapted and spaces. 相似文献
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In this paper, we classify -Nambu structures via -cohomology. The complex of -forms is an extension of the De Rham complex, which allows us to consider singular forms. -Cohomology is well understood thanks to Scott (2016) [12], and it can be expressed in terms of the De Rham cohomology of the manifold and of the critical hypersurface using a Mazzeo–Melrose-type formula. Each of the terms in -Mazzeo–Melrose formula acquires a geometrical interpretation in this classification. We also give equivariant versions of this classification scheme. 相似文献
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A sufficiently regular hypersurface immersed in the -dimensional Euclidean space is determined up to a proper isometry of by its first and second fundamental forms. As a consequence, a sufficiently regular hypersurface with boundary, whose position and positively-oriented unit normal vectors are given on a non-empty portion of its boundary, is uniquely determined by its first and second fundamental forms. We establish here stronger versions of these uniqueness results by means of inequalities showing that an appropriate distance between two immersions from a domain ω of into is bounded by the -norm of the difference between matrix fields defined in terms of the first and second fundamental forms associated with each immersion. 相似文献
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《Applied Mathematics Letters》2005,18(11):1286-1292
First a general model for two-step projection methods is introduced and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let be a real Hilbert space and be a nonempty closed convex subset of . For arbitrarily chosen initial points , compute sequences and such that where is a nonlinear mapping on is the projection of onto , and . The two-step model is applied to some variational inequality problems. 相似文献
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Andrea Luigi Tironi 《Discrete Mathematics》2018,341(11):3152-3158
Let be a hypersurface in with defined over a finite field of elements. In this note, we classify, up to projective equivalence, hypersurfaces as above which reach two elementary upper bounds for the number of -points on which involve a Thas’ invariant. 相似文献